Publications

Preprints

    1. K. Vilonen and T. Xue, A note on Hessenberg varieties. arxiv: 2101.08652.
    2. M. Grinberg, K. Vilonen, and T. Xue, Nearby Cycle Sheaves for Stable Polar Representations, arXiv:2012.14522.
    3. K. Vilonen, and T. Xue, Character sheaves for graded Lie algebras: stable gradings, arXiv:2012.08111.
    4. K. Vilonen, and T. Xue, Character sheaves for symmetric pairs, arXiv:1806.02506.
    5. M. Grinberg, K. Vilonen, and T. Xue, Nearby cycle sheaves for symmetric pairs, arXiv:1805.02794.
    6. R. Bezrukavnikov and K. Vilonen, Koszul Duality for Quasi-split Real Groups, arXiv:1510.08343.
    7. S. Gelfand, R. MacPherson, and K. Vilonen, Microlocal Perverse Sheaves, arXiv:0509440.

Publications

    1. T.-H. Chen, K. Vilonen and T. Xue, Springer correspondence, Hyperelliptic curves, and cohomology of Fano varieties. Math. Res. Lett. 27 (2020), No. 5, 1281-1323. arXiv.
    2. T.-H. Chen, K. Vilonen and T. Xue, Hessenberg varieties, intersections of quadrics, and the Springer correspondence, Trans. Amer. Math. Soc. 373 (2020), No. 4, 2427-2461. arXivMR4069224
    3. J. Taskinen and K. Vilonen, Cartan theorems for Stein manifolds over a discrete valuation baseJ. Geom. Anal. 29 (2019), No. 1, 577-615. arXivMR3897027
    4. T. -H. Chen, K. Vilonen and T. Xue, Springer correspondence for the split symmetric pair in type ACompos. Math. 154 (2018), No. 11, 2403-2425. arXiv. MR3867304
    5. I. Mirkovic and K. Vilonen, Erratum for “Geometric Langlands duality and representations of algebraic groups over commutative rings”, Ann. of Math. (2) 188 (2018), No. 3, 1017-1018. MR3866890
    6. T.-H. Chen, K. Vilonen and T. Xue, On the cohomology of Fano varieties and the Springer correspondence, With an appendix by Dennis Stanton. Adv. Math. 318 (2017), 515-533. arXiv. MR3689749
    7. T. Xue and K. Vilonen, The null-cone and cohomology of vector bundles on flag varieties, Represent. Theory 20 (2016), 482-498. MR3589334
    8. W. Schmid and K. Vilonen, Hodge theory and unitary representations, Representations of reductive groups, Progr. Math. 312, Birkhäuser/Springer, Cham (2015), 443-453. MR3495806
    9. M. Kashiwara and K. Vilonen, Microdifferential systems and the codimension-three conjecture, Ann. of Math. (2) 180 (2014), 573-620. MR3224719
    10. K. Vilonen and G. Williamson, Characteristic cycles and decomposition numbers, Math. Res. Lett. 20 (2013), 359-366. MR3151652
    11. W. Schmid and K. Vilonen, Hodge theory and unitary representations of reductive Lie groups, Frontiers of Mathematical Sciences, International Press (2011), 397-420, arXiv. MR3050836
    12. M. Kashiwara and K. Vilonen, On the codimension-three conjecture, Proc. Japan, Acad., Ser. A 86 (2010), 154-158. MR2780007
    13. I. Mirkovic and K. Vilonen, Geometric Langlands duality and representations of algebraic groups over commutative rings, Annals of Math., 166 (2007), 95-143. MR2342692
    14. M. Emerton, D. Nadler, and K. Vilonen, A geometric Jacquet functor, Duke Math. J. 125 (2004), No. 2, 267-278. arXiv. MR2096674
    15. E. Frenkel, D.Gaitsgory, and K. Vilonen, On the geometric Langlands conjecture, Journal of Amer. Math. Soc., 15 (2002), No. 2, 364-417. MR1887638
    16. E. Frenkel, D. Gaitsgory and K. Vilonen, Whittaker patterns in the geometry of moduli spaces of bundles on curves, Annals of Math. 153 (2001), 699-748. arXiv. MR1836286
    17. W. Schmid and K. Vilonen, Characteristic cycles and wave front cycles of representations of reductive groups, Annals of Math. 151 (2000), 1071-1118. arXiv. MR1779564
    18. I. Mirkovic and K. Vilonen, Perverse Sheaves on Affine Grassmannians and Langlands Duality, Mathematical Research Letters 7 (2000), 13-24. MR1748284
    19. W. Schmid and K. Vilonen, On the geometry of nilpotent orbits, Asian J. Math., vol 8, no 1 (1999), 233-274, A Special Volume in Honour of Sir Michael Atiyah.
      Reprinted in – Surveys in differential geometry, Surv. Differ. Geom., VII, Int. Press (2000), 565-623. MR1919437
    20. K. Vilonen, Geometric methods in representation theoryRepresentation theory of Lie groups, Amer. Math. Soc. (1998), 241-290. MR1737730
    21. K. Vilonen, Topological methods in representation theory, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 595–604. MR1648108
    22. W. Schmid and K. Vilonen, Two geometric character formulas for reductive Lie groups, Journal of AMS, 11 (1998), No. 2, 799-876. MR1612634
    23. E. Frenkel, D.Gaitsgory, D. Kazhdan, and K. Vilonen, Geometric realization of Whittaker Functions and the Langlands Conjecture, Journal of AMS, 11 (1998), No. 2, 451-484. MR1484882
    24. S. Gelfand, R. MacPherson, and K. Vilonen, Perverse sheaves and quivers, Duke Math. Journal 83 (1996), 621-643. MR1390658
    25. W. Schmid and K. Vilonen, Characteristic cycles of constructible sheaves, Invent. Math. 124 (1996), 451-502. MR1369425
    26. W. Schmid and K. Vilonen, Characters, characteristic cycles, and nilpotent orbits. Geometry, Topology & Physics (1995), 329-340. MR1358623
    27. W. Schmid and K. Vilonen, Weyl group actions on Lagrangian cycles and Rossmann’s formula. Noncompact Lie groups and some of their applications (San Antonio, TX, 1993), 243–250, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 429, Kluwer Acad. Publ., Dordrecht, 1994. MR1306528
    28. K. Vilonen, Perverse sheaves and finite-dimensional algebras, Trans. Amer. Math. Soc. 341 (1994), 665-676. MR1135104
    29. W. Schmid and K. Vilonen, Characters, fixed points and Osborne’s conjecture, Representation theory of groups and algebras, Amer. Math. Soc. (1993), 287-303. MR1216196
    30. I. Mirkovic, T. Uzawa and K. Vilonen, Matsuki correspondence for sheaves, Invent. Math. 109 (1992), No. 2, 231-245. MR1172690
    31. I. Mirkovic and K. Vilonen, Characteristic varieties of character sheaves, Invent. Math. 93 (1988), No. 2, 405-418. MR0948107
    32. R. MacPherson and K. Vilonen, Perverse sheaves with singularities along the curve y^n=x^m, Comment. Math. Helv. 63 (1988), No. 1, 89-102. MR0928029
    33. R. Mirollo and K. Vilonen, Bernstein-Gel’fand-Gel’fand reciprocity on perverse sheaves, Ann. Sci. Ecole Norm. Sup. (4) 20 (1987), No. 3, 311-323. MR0925719
    34. R. MacPherson and K. Vilonen, Elementary construction of perverse sheaves, Invent. Math. 84 (1986), No. 2, 403-435. MR0833195
    35. K. Vilonen, Intersection homology D-module on local complete intersections with isolated singularitiesInvent. Math. 81 (1985), No. 1, 107-114. MR0796193
    36. R. MacPherson and K. Vilonen, Elementary construction of perverse sheaves (French), C.R.Acad. Sci. Paris Ser. I. Math. 299 (1984), No, 10, 443-446. MR0768077